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Solved: Museum management. Refer to the Museum Management
Chapter 3, Problem 16E(choose chapter or problem)
Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 2.14 (p. 50). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. A summary of the results is reproduced in the table.
\(\begin{array}{lc}
\hline \text { Performance Measure } & \text { Number of Museums } \\
\hline \text { Total visitors } & 8 \\
\text { Paying visitors } & 5 \\
\text { Big shows } & 6 \\
\text { Funds raised } & 7 \\
\text { Members } & 4 \\
\hline
\end{array}\)
a. If one of the 30 museums is selected at random, what is the probability that the museum uses total visitors or funds raised most often as a performance measure?
b. Consider two museums of contemporary art randomly selected from all such museums. Of interest is whether or not the museums use total visitors or funds raised most often as a performance measure. Use a tree diagram to aid in listing the sample points for this problem.
c. Assign reasonable probabilities to the sample points of part b. [Hint: Use the probability, part a, to estimate these probabilities.]
d. Refer to parts b and c. Find the probability that both museums use total visitors or funds raised most often as a performance measure.
Questions & Answers
QUESTION:
Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 2.14 (p. 50). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. A summary of the results is reproduced in the table.
\(\begin{array}{lc}
\hline \text { Performance Measure } & \text { Number of Museums } \\
\hline \text { Total visitors } & 8 \\
\text { Paying visitors } & 5 \\
\text { Big shows } & 6 \\
\text { Funds raised } & 7 \\
\text { Members } & 4 \\
\hline
\end{array}\)
a. If one of the 30 museums is selected at random, what is the probability that the museum uses total visitors or funds raised most often as a performance measure?
b. Consider two museums of contemporary art randomly selected from all such museums. Of interest is whether or not the museums use total visitors or funds raised most often as a performance measure. Use a tree diagram to aid in listing the sample points for this problem.
c. Assign reasonable probabilities to the sample points of part b. [Hint: Use the probability, part a, to estimate these probabilities.]
d. Refer to parts b and c. Find the probability that both museums use total visitors or funds raised most often as a performance measure.
ANSWER:Step 1 of 6
(a)
Find the probability that the museum uses the most often performance measure as total visitors or funds raised.
The experiment is to evaluate the performance of the museum. Here, the performance measures are considered as the sample points. Also, the total number of museums is 30. The number of museums corresponding to each sample point and its corresponding reasonable probabilities are tabulated below:
|
Performance Measure |
Number of Museums |
Assignable Probabilities |
|
Total visitors |
8 |
\(\frac{8}{30}\) |
|
Paying visitors |
5 |
\(\frac{5}{30}\) |
|
Big shows |
6 |
\(\frac{6}{30}\) |
|
Funds raised |
7 |
\(\frac{7}{30}\) |
|
Members |
4 |
\(\frac{4}{30}\) |
Table (1)
From Table (1), it is clear that that the total number of museums is 30. Also, the number of museums under total visitors and funds raised are 8 and 7, respectively. Thus, the probability is calculated as given below:
\(\begin{aligned}
P(\text { Total visitors or Funds raised }) & =P(\text { Total visitors })+P(\text { Funds raised }) \\
& =\frac{8}{30}+\frac{7}{30} \\
& =\frac{15}{30} \\
& =0.5
\end{aligned}\)
Thus, the probability that the museum uses the most often performance measure as total visitors or funds raised is 0.50.